QSymAlgebra

The degree-$n$ graded piece of QSym — one basis element per composition of $n$, $2^{n-1}$ of them for $n \geq 1$.

QSymAlgebra(n)the degree-$n$ piece of QSym

Typed signatures

Type	Package	Applies
(integer) -> graded_hopf_algebra	hopf	always

Domain: Hopf algebras

Examples

Basic #

$2^{5-1}$ compositions

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In$\mathrm{AlgebraDimension}(\mathrm{QSymAlgebra}(5))$Out$16$

The monomial basis

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In$\mathrm{Basis}(\mathrm{QSymAlgebra}(3))$Out$\bigl\lbrack\mathrm{QSymM}(\bigl\lbrack1, 1, 1\bigr\rbrack), \mathrm{QSymM}(\bigl\lbrack1, 2\bigr\rbrack), \mathrm{QSymM}(\bigl\lbrack2, 1\bigr\rbrack), \mathrm{QSymM}(\bigl\lbrack3\bigr\rbrack)\bigr\rbrack$

About

Examples	2

See also: QSymM, NSymAlgebra